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Tuning Digest # 207
postings by Joe Monzo
Tue, 8 June 1999 00:26:27 -0500 (EST)
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From: monz@juno.com
Many thanks to Margo for her extremely informative post about
medieval instrumental music. Apologies for the inordinate length
of this response. This is partly the result of quoting Margo's
already long post in its entirety, but that was so tightly
organized that I couldn't bring myself to omit any of it, and
hopefully I will be forgiven for my excess.
[Margo Schulter, TD 206.14:]
OK, I'll accept your thanks and respond with 'you're welcome'.
But in truth, since I get the postings in Digest form, I wasn't
actually calling it to your attention specifically. I was
responding directly to Bill myself, and had sent my post long
before I ever read yours. As you yourself pointed out here
once, sometimes the nature of email leads to unintended
miscommunication. Certainly not a big deal in any case. :)
[Schulter:]
In connection with this comment, I'd like to quote Richard H.
Hoppin, 1978, Medieval Music, from the chapter Polyphony in
the 13th Century, p 347-349, concerning the time-period about a
century prior to that of which you speak further on. Hoppin is
here discussing the very end of the Ars Antiqua [c. 1300]:
[Hoppin:]
Most of the references to instrumental performance, either in
poems or in theoretical treatises, are concerned with monophonic
songs and dances. It is probable, however, that players
provided troubadour and trouvere songs with simple improvised
accompaniments. We have also noted the likelihood that
instruments took over the performance of motet tenors and thus
introduced accompanied duets and trios as well as solo songs.
Instrumental doubling of the vocal lines is a further probability
from which it is but a short step to the substitution of
instruments for voices. It has been suggested that the caudae
of conducti were designed for instrumental performance and 'may
prove to be a valuable source for 13th-century dance music' [New
Oxford History of Music, 1954, vol 2, p 337]. Such an assumption
is a bit farfetched, perhaps, but vocal polyphony undoubtedly did
provide music for instrumental ensembles. A few pieces in vocal
forms even appear to have been intended for instrumental
performance.
...
[for example:] ...the 'instrumental motets' in the Bamberg Codex
(# 102-108). ...Like the later secular motets, these pieces would
seem to have lost all connection with organum, and their textless
state, together with their use of hocket, makes the assumption of
instrumental performance unavoidable.
I'd be very interested in seeing some studies done on the
intonations implied by the design of medieval and Renaissance
woodwind instruments. As a former woodwind player myself,
and with the current increased interest in using 'historical
instruments' in performance and recording, I'm surprised that
this hasn't been done (or perhaps I just don't know about it
- from those who know, references would be appreciated)
[Schulter:]
Lindley also shows how, around 1400-1450, keyboard sources such
as the Italian Faenza Codex and the German Buxheimer Organ Book
used prominent sonorities with schisma thirds as a very popular
"special effect," indeed sometimes a "stock in trade," as he
puts it. While the "explosion" in lute and keyboard tablatures
around 1500 was yet to come, these trends may have played a role
in the stylistic change around 1420-1450 which marked what
Tinctoris (1477) regarded as the beginning of truly "modern"
music. In current historical terms, this is often regarded as
the Gothic/Renaissance transition.
What Hoppin says at the end of Medieval Music, p 522-524, has
a direct bearing on some of the points you make here, as well as
on the question of tuning in general, and England's role:
[Hoppin:]
...we can only admire the poet's acuity of critical judgment in
putting his finger on the one aspect of English music -- and of
Dunstable's in particular -- that was chiefly responsible for
its influence on continental composers... a new treatment of
consonance and dissonance...[which] began when composers rejected
medieval permissiveness in the combination of harmonic intervals
in favor of a 'panconsonant' style that required each voice to
be consonant with all the others. Hand in hand with this
elimination of dissonance from the essential tones of vertical
combinations went a much more restricted and controlled use of
dissonance to ornament the harmonic tones. The unprepared and
accented dissonances so characteristic of 14th-century music now
disappear almost entirely.
...
We must recognize Dunstable as the greatest English composer
of his day. We must also recognize that, for perhaps the only
time, the prestige and influence of English composers changed
the course of music history thru-out western Europe. By these
recognitions we confirm the judgment of Tinctoris, altho we may
rephrase his statement to make English composers, with Dunstable
at their head, the fount and origin of the musical Renaissance.
In their works, and in the works of continental contemporaries
who added the English countenance to their earlier mixture of
French subtilitas with Italian dulcedo, music moves beyond
the scope of the present study. For the music of the Middle
Ages, the end had come.
IMO, Hoppin may be making a few rather broad generalizations,
and I believe he's British, so there may be a bit of patriotic fervor
expressed here.
But overall I think these comments by another expert on medieval
music provide pretty good evidence that 'sweetening' of '3rds'
and '6ths' (from 3- to 5-limit ratios) had long been an important
part of English musical performance, especially if one considers
both the writings of Odington and Theinred and the observation
I've been making about the lag of theoretical description behind
musical practice.
In connection with this, it's interesting to consider the
heterogenous ethnic base of medieval England, a mixture of the
original inhabitants, and successive waves of Celtic, Roman,
German (Anglo-Saxon, then Danish, then Norwegian), and finally
Norman (= Celtic + Roman + German [Frank] + Norwegian) invaders.
I wonder if this had anything to do with intonational preferences
or their evolution?
The fact that the shift from 3- to 5-limit was noticed by Theinred
so soon (little more than a century) after the Norman invasion of
1066 seems to me to indicate either that the people already living
in England before that may have been using 5-limit harmonies, or,
still more likely, that it was a characteristic shared by the
inhabitants of both England and Normandy.
This might lead one to believe that perhaps it springs
ultimately from unrecorded sources in Scandinavia. The presence
of the Vikings would be the main ethnic differentiation between
England/Normandy and the rest of literate Europe around 1100.
And the Vikings had sailed to America just before this, so perhaps
they got 5-limit from Native Americans? I'm speculating wildly
here, but 5-limit singing does seem to have suddenly appeared
shortly after this in the Anglo-Norman lands, and there is the
possibility...
Can anyone give some insight into the earliest manuscripts of
Scandinavian compositions or theoretical treatises?
[Schulter:]
During the first half of the 16th century, an incredible
flowering of instrumental forms occurred, ranging from dances
and improvisatory lute and keyboard preludes to Willaert's
ensemble ricarcare. By 1555, Vicentino was prepared to
advocate the use of his 31-tet archicembalo as a standard
for intonation by singers.
In discussing either the 3-limit JI of the Gothic era or the
5-limit JI of the Renaissance, it may be helpful to remember
that these are ideals of intonation, guiding singers of some
natural variability in their intervals. In performances involving
mixed voices and instruments, common for example in the various
Florentine entertainments chronicled by Howard Mayer Brown,
instrumental and vocal intonations would interact, making the
former not irrelevant.
As early as 1516, by which year Castiglione's Courtier is said
to have been completed (it was published in 1528), an author
argues that the most pleasing court music is a vocal solo
accompanied by the viola a mano -- that is, actually, a lute
or similar plucked instrument. Various Italian frottole around
1500 may have performed in this manner, and arrangements of
Italian madrigals by Verdelot, for example, for the lute may
have represented a continuation of this tradition.
This is not at all to minimize the importance of the view taken
by various theorists of the later 16th century that there are
three distinct types of intonation: (1) Just intonation for
voices, specifically 5-limit; (2) Meantone for keyboards; and
(3) 12-tet for lutes. However, in forms where these varieties
of instruments (the voice being considered the most "perfect")
interacted, mutual influence or accommodation might come into
play.
The influence of instrumental intonations in practice is
suggested by Vicentino, who describes the conventional practice
of his time as "mixed and tempered music." The "mixed" refers
to his view that even compositions typically classified as
"diatonic" in fact use elements of the chromatic and enharmonic
genera; and the "tempered" evidently refers to the kind of
accommodations made in meantone tunings for keyboard.
Hmmm... Now your comments about 'mutual influence or accommodation'
have got me wondering about the possible role of well-temperaments
during the Renaissance, whereas they are usually associated with
the Baroque period which followed.
From Anthony Baines, 1961, Musical Instruments Through the Ages,
chapter 7, 'The Fretted Instruments':
[Baines:]
In this same chapter, Michael W. Prynne [in his article
I. The Lute] calls John Dowland 'the greatest lutenist of
his day'.
These statements, on the tremendous popularity of the lute
in general and Dowland in particular during the 1500s and early
1600s, make me wonder just how widespread Dowland's lute tuning
[published 1610] may have been.
This tuning, as opposed to the lute tunings generally cited, was
most emphatically not 12-eq, but rather a complex rational
system (I hesitate to call it JI, as it includes no 5-limit ratios)
which functioned as a well-temperament. See my Dowland webpage:
http://www.ixpres.com/interval/monzo/fngrbds/dowland/dowland.htm
I'm also very curious as to exactly how and why Dowland chose
the particular ratios he used in this system.
Does anyone have any clues?
[Schulter:]
In medieval versions of the Pythagoras story, this theorist heard
an amazingly harmonious striking of blacksmith's hammers, and the
set out to investigate how this could come about. Such curiosity
led to experimentation, and the discovery of the ratios of the
principal concords. Thus the sense of hearing and the intellect
are partners in the kind of theorizing advocated by Pythagoreans
such as Jacobus of Liege: concord and discord themselves are
described in terms of smoothly blending or roughly "colliding"
sounds, as well as in terms of numerical ratios.
Further, to such medieval theorists, concord/discord
classifications reflect style as well as mathematics. For
Jacobus, while stable concords are generally limited to the
classic 3-(odd)-limit intervals, a variety of other intervals
are also recognized as "medial" or "imperfect" concords. These
include the major third (81:64), minor third (32:27), major
second (9:8), minor seventh (16:9), and major sixth (27:16).
Not all of these ratios are mathematically so tidy, but
Jacobus hears the intervals as more or less blending, and so
describes them as "concordant" to various degrees.
Possibly the hallmark of "Pythagoreanism" in such a medieval
setting is a desire to explain artistic perceptions in a
precisely quantitized way -- something rather different from
considering such perceptions irrelevant. Thus in the early 15th
century, Prosdocimus portrays his fellow Paduan theorist
Marchettus of about a century earlier as a very bad
mathematician, but a good practical musician. In fact, without
necessarily joining with Prosdocimus in his value judgment, one
can say that the mathematics of Marchettus are at best a bit
unclear, as compared with the 17-note Pythagorean scheme of the
later theorist.
I can certainly agree with you that Marchetto's mathematics are unclear;
however, he was no longer alive to defend himself against Prosdocimus's attacks,
and so there was never any clarification. My attempt to do so:
http://www.ixpres.com/interval/monzo/marchet/marchet.htm
leads me to believe that Marchetto's mathematical ideas may actually have
been quite sophisticated and ingenious; unfortunately, if I am correct,
he did express those ideas badly, which led to centuries of confusion
and misrepresentation of his possibly brilliant theories.
[Schulter:]
In my view, our answer might depend on how "perceptible" is
interpreted. Certainly it is possible for an attuned listener
to discern this difference of a Pythagorean comma (~23.46 cents),
but at the same time, one might guess that in the early 15th
century, as now, many listeners might find either interval an
acceptable representative of the "major sixth" class. Indeed,
keyboard works of the period which in popular keyboard tunings
would use both flavors of sixths lend support to this view.
Your points here are very well taken, and I don't find them at
all contradictory to my views. On the contrary, I'm coming to
believe more and more that a wide variety of tunings have
always been in use in music, from all chronological periods and
in all geographical locations, and that various different
tunings of particular intervals have always been accepted by
listeners as embodying that interval's gestalt.
I likened this once before, in a posting, to the recognition
by linguists of the concept of a phoneme, where a particular
language's rules accept or ignore specific phonetic elements
as embodying meaninful linguistic content, and where these
rules of acceptance/ignorance change according to the language
under consideration.
I think a musical style is analagous to a language in the
same way, where specific phonetic elements would be analagous
to specific tunings of intervals, and phonemes would be
analagous to the general intervallic gestalt. What is
accepted or ignored as carrying meaning would change according
to the musical style under consideration.
I think this idea provides a fruitful avenue for further
research.
[Schulter:]
I would like to comment here on your last clause, inasmuch as
I'm the one who posted recently on that subject.
I was referring specifically to Ptolemy's views of strict
Pythagorean theory being 'numbers divorced from acoustical
reality'. Ptolemy's attempts to reconcile the Pythagorean
(rational) and Aristoxenean (irrational) approaches was probably
a result of the neo-Pythagorean revival of his day.
From the evidence of Ptolemy's treatise, theorists c. 100 AD had
enthusastically re-embraced Pythagorean theory, and, his empirical
results not jiving with this, Ptolemy sought to include the more
musically empirical theories of Aristoxenus.
I did not mean to imply that this attitude towards Pythagorean
theory is valid for the medieval period, or that it was held
by medieval theorists themselves. I humbly bow before your
expertise in this area.
A point that I was making in earlier posts which I would like
to reiterate:
The mathematical descriptions of tunings by theorists of the
1300-1500s became proportionately more accurate and more complex
as these theorists became increasingly well acquainted with
ancient Greek treatises which used non-Pythagorean ratios
and, in the case of Aristoxenus, non-rational measurements.
However, this does not necessarily reflect the actual state of
musical practice before 1300 as using less complex tunings.
As I said, descriptive music-theory always lags (sometimes far)
behind practice.
(And please note that this statement does not pertain to
proscriptive theories like those of Yasser or Partch.)
If there's any certain conclusion I can make based on research
I've done for my book, it's that high-prime ratios have been
used in describing musical intervals since virtually the beginning
of our extant documents.
To: tuning@onelist.com
Date: Mon, 7 Jun 1999 18:01:01 -0400
Subject: Medieval instrumental music & early 5-limit
First, I'd much like to thank Joe Monzo for calling to my
attention that Salinas published his 1/3-comma meantone tuning
(and also a very interesting just intonation scheme) in 1577,
not 1571 as I surmised in a response to Bill Alves.
Secondly, as to the role of instrumental music in late medieval
and Renaissance Europe, I would certainly agree that vocal music
is both the prevalent form and the "perfect" ideal of these eras.
However, this does not mean that instrumental music was
inconsequential, or that its influence on vocal intonations was
necessarily negligible.
The dearth of manuscript evidence for instrumental music in
the Middle Ages is both astonishing and mysterious. Writers
and theorists make countless references to instruments and
their practical uses. Manuscript illustrations and cathedral
sculptures depict a wide variety of instruments, often in
connection with singing or dancing, but sometimes in ways that
suggest either solo or ensemble performances. Peasants
reportedly played instruments for their rustic dances.
Jongleurs were expected to play as many as ten instruments
according to the Conseils aux Jongler written by Guiraut de
Calanson in 1210. Troubadours and trouveres presumably sang
their songs to instrumental accompaniment. In short, there
is abundant evidence that instruments played a vital role in
medieval musical life at every social level, yet only a handful
of purely instrumental pieces has been preserved. Several
factors probably account for this situation. Instrumental
performance seems to have been largely the province of jongleurs,
whose music has either been lost or, as is more likely, was never
written down. Peasants too probably had a repertory of both song
and dance tunes that were passed on solely by oral tradition.
And at all levels of society, apparently, vocal music provided
the chief source of material for instrumental performance.
Numerous poems speak of musicians playing chansons or lais or
ballades on a variety of instruments, and Johannes de Grocheo
says that 'a good artist plays on the viol every cantus and
cantilena and every musical form in general' [quoted in
Gustave Reese, 1940, Music in the Middle Ages, p. 327].
(email me)
Mark Lindley, for example, argues with due caution that the new
modified Pythagorean tunings of the early 15th century, possibly
sometimes implemented on keyboards with more than 12 notes per
octave, may have influenced the vocal writing of composers such
as Dufay, intriguing them with the sound of nearly pure schisma
thirds involving written sharps.
If Dunstable [?-1453] was in [the Duke of] Bedford's service on
the continent, as we must assume he was, he would have had ample
opportunities for meeting and influencing musicians at the
Burgundian court. A contemporary poet, Martin le Franc, bears
witness ... in ... Le Champion des dames) [1441-2]. After
proclaiming the superiority of Dufay and Binchois over their
French predecessors, le Franc credits their excellence to their
having followed Dunstable and adopted the 'English countenance',
by which means they found a new way of using 'sprightly concords'
to create song of marvelous pleasure, joyous and memorable.
(email me)
While the formal vocal forms of sacred and secular polyphony
continued to hold center stage in the 16th century, instrumental
forms played a very important role also, and madrigals, for
example, might be sometimes be performed by mixed consorts of
voices and instruments. In fact, the complications and conflicts
resulting from such mixed ensembles (e.g. meantone keyboards and
12-tone equal temperament or 12-tet lutes) was one topic of
discussion in late 16th-century treatises.
four centuries ago [c. 1561] the place of the lute in musical
life in many ways foreshadowed that of the pianoforte in modern
times [1961], both as the chief instrument of the home and as
the first instrument for the professional virtuoso of
international fame.
(email me)
Because the topic of the Pythagorean-Aristoxenian-Ptolemaic
debate is often raised here, I would like to conclude with one
point about at least the late medieval theorists of polyphony
and Pythagorean tuning. This really isn't addressed to any one
previous article in particular, but maybe to a general trend of
thought.
Further, as Prosdocimus shows, it is quite possible to champion
a Pythagorean approach to intonation while showing an awareness
of the role of perception. Thus, having recognized the
distinction between intervals such as A3-F#4 (major sixth, 27:16)
and A3-Gb4 (diminished seventh, 32768:19683), he wonders aloud
whether this distinction might be "imperceptible" to the ear.
Here I wish not at all to minimize the importance of our ongoing
dialogue regarding the traditions of Pythagorus, Ptolemy, and
Aristoxenes, only to caution against any blanket equation of
"Pythagorean" theory during the medieval period with an
indifference to the evidence of the senses or to the vital
dynamics of style.
Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------
|
or try some definitions. |
I welcome
feedback about this webpage:
|